$$ \begin{aligned} -8 &= \frac{k}{10}-7&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10\cdot(-8) &= 10 \cdot \frac{k}{10}-10\cdot7&& \text{cancel out the denominators} \\[1 em]-80 &= k-70&& \text{ swap the left and right side of the equation } \\[1 em]k-70 &= -80&& \text{ move -70 to the right } \\[1 em]k &= -80+70&& \\[1 em]k &= -10&& \\[1 em]k &= -10&& \\[1 em] \end{aligned} $$

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